A025609 Number of n-move rook paths on 8 X 8 board from given corner to adjacent corner.

0, 1, 6, 64, 720, 9136, 122016, 1673344, 23216640, 323773696, 4525272576, 63308468224, 886046453760, 12403017773056, 173632453287936, 2430795572936704, 34030785382318080, 476428879520137216, 6669991618287108096, 93379806486052470784, 1307316833784928665600

Offset

0,3

Comments

Paths are not required to be self-avoiding. - Andrew Howroyd, Nov 05 2019

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (18,-44,-168).

Formula

G.f.: x*(1 - 12*x)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)).

a(n) = 18*a(n-1) - 44*a(n-2) - 168*a(n-3) for n >= 3.

Mathematica

CoefficientList[ Series[(x - 12 x^2)/((1 + 2 x) (1 - 6 x) (1 - 14 x)), {x, 0, 16}], x]

Prog

(PARI) concat([0], Vec((1 - 12*x)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20)))

Crossrefs

Cf. A025607, A025608.

Sequence in context: A237357 A230282 A186668 * A309186 A156887 A239847

Adjacent sequences: A025606 A025607 A025608 * A025610 A025611 A025612

Keyword

nonn,walk

Author

David W. Wilson

Extensions

Terms a(17) and beyond from Andrew Howroyd, Nov 05 2019

Status

approved